Problem: If $x \dagger y = x^{2}-2y^{2}$ and $x \star y = (6-x)(y)$, find $(-3 \star 1) \dagger 6$.
First, find $-3 \star 1$ $ -3 \star 1 = (6-(-3))(1)$ $ \hphantom{-3 \star 1} = 9$ Now, find $9 \dagger 6$ $ 9 \dagger 6 = 9^{2}-2(6^{2})$ $ \hphantom{9 \dagger 6} = 9$.